Theme Essential Question: How do we use scatter plots to create predictions of real world data by analyzing relationships or associations, between two quantities considering outliers and clusters?
Essential Questions: How can you use a trend line to make a prediction from a scatter plot?
Standards
8. SP.2Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8. SP.3Use the equation of a linear model to solve problems in the context of bivariate (having two variables) measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
Objectives
The students will use proper technique to draw a trend line to model data displayed in a scatter plot.
The student will generate an equation for the trend line that models bivariate data.
The student will use a trend line to make predictions, to include interpreting the slope of the line and y-intercept.
Assessment Product
During this lesson, the students will continue preparing their presentation on the website assigned. They should prepare their table (if not given), draw a trend line and generate the equation for the trend line. They should begin to discuss questions (assigned or found relevant) leading to the needed predictions using the interpretation of the slope and y-intercept.
Key Questions
Why are outliers disregarded when drawing a trend line?
What factors should be considered in drawing a trend line?
How can you use the equation of a trend line to make predictions?
What is the difference between interpolation and extrapolation and how are they used in making predications?
Observable Student Behaviors
The student can use a viable strategy to draw a trend line for a scatter plot.
The student can generate an equation for the trend line.
The student can use a table, graph, and/or equation of the trend line to make predictions.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary Bivariate data, scatter plot, cluster, outlier, association (correlation), interpolation, and extrapolation
Suggested Activities [see Legend to highlight MCO and HYS]
On Core Mathematics Unit 6.2, p. 149-152
ABC Mastering the Common Core in Mathematics, Chapter 8.2- 8.6 p. 112-118
Gizmo Lessons
8.SP.2
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
Solving Using Trend Lines
Examine the scatter plots for a data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best‑fit line.
8.SP.3
Determining a Spring Constant
Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
A set of ten practice problems focusing on association and predictions.
Highly Recommended:
http://illustrativemathematics.org/standards/k8 (SP.2)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Exploring the relationship between data sets and linear equations.
8. SP.2 Reasoning: Limitations of Assumptions
This activity covers how to develop a model from a limited data set based on assumptions and analyze the effect of the assumptions on conclusions in the model.
8. SP.3 What’s My Line
Exploring the relationship between data sets and linear equations.
Content: Scatter Plots and Predictions
Dates: 2/11-2/16
Theme Essential Question:
How do we use scatter plots to create predictions of real world data by analyzing relationships or associations, between two quantities considering outliers and clusters?
Essential Questions:
How can you use a trend line to make a prediction from a scatter plot?
Standards
Objectives
Assessment
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Bivariate data, scatter plot, cluster, outlier, association (correlation), interpolation, and extrapolation
Suggested Activities [see Legend to highlight MCO and HYS]
- On Core Mathematics Unit 6.2, p. 149-152
- ABC Mastering the Common Core in Mathematics, Chapter 8.2- 8.6 p. 112-118
- Gizmo Lessons
- 8.SP.2
- Correlation
- Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
- Solving Using Trend Lines
- Examine the scatter plots for a data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best‑fit line.
- 8.SP.3
- Determining a Spring Constant
- Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.
- Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
- 8.SP.2 p. 239
- 8.SP.3 p. 241
- JBHM 8th GP3- p. 220-221 and p. 236-338
- Glencoe Pre-Algebra- p. 298-303
- http://www.mytestbook.com/worksheet.aspx?test_id=1385&grade=8&subject=Math&topics=Probability%20and%20Statistics%20Scatter%20Plot
- A set of ten practice problems focusing on association and predictions.
- Highly Recommended:
http://illustrativemathematics.org/standards/k8 (SP.2)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Diverse Learners
Homework
Suggested:
Terminology for Teachers
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
- See New York Common Core Aligned Task (other resources)
http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htmArt, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
- Smartboard Resource Website
- 8. SP.2 What’s My Line
Exploring the relationship between data sets and linear equations.- 8. SP.2 Reasoning: Limitations of Assumptions
This activity covers how to develop a model from a limited data set based on assumptions and analyze the effect of the assumptions on conclusions in the model.- 8. SP.3 What’s My Line
Exploring the relationship between data sets and linear equations.Websites
Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Matrix
Week 1
Week 2
Week 3
Week 4
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4